What if you wanted to compare the steepness of two roofs? After completing this Concept, you'll be able to determine the steepness of lines in the coordinate plane using what you learned in Algebra I about slope.

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Guidance

Recall from Algebra I, the slope of the line between two points
and
) is
.

Different Types of Slope
:

Example A

What is the slope of the line through (2, 2) and (4, 6)?

Use the slope formula to determine the slope. Use (2, 2) as
and (4, 6) as
.

Therefore, the slope of this line is 2. This slope is positive.

Example B

Find the slope between (-8, 3) and (2, -2).

This is a negative slope.

Example C

Find the slope between (-5, -1) and (3, -1).

Therefore, the slope of this line is 0, which means that it is a horizontal line. Horizontallines always pass through the
axis. Notice that the
coordinate for both points is -1. In fact, the
coordinate for
any
point on this line is -1. This means that the horizontal line must cross
.

Example D

What is the slope of the line through (3, 2) and (3, 6)?

Therefore, the slope of this line is undefined, which means that it is a
vertical
line. Vertical lines always pass through the
axis. Notice that the
coordinate for both points is 3. In fact, the
coordinate for
any
point on this line is 3. This means that the vertical line must cross
.